The media mogul's implication that the U.S. should have a pause on allowing refugees into the country while it "fixes vetting" is not a new idea. The House of Representatives recently voted to ban Syrian and Iraqi refugees from entering the U.S., calling for tougher screening measures.

However, Trump's request to bar all Muslims from entering the country has been met with indignation and disdain.

Hours after his initial post, Murdoch said he was "NOT endorsing Trump, but support Congressional vote for immediate pause to overhaul vetting process." That position is not the same as a ban on all Muslims coming to America.

NOT endorsing Trump, but support Congressional vote for immediate pause to overhaul vetting process.

Murdoch backing Trump on Tuesday was somewhat unusual as the media mogul has been critical of the GOP candidate in the past, especially on his immigration views. In July, Murdoch said Trump was "wrong" about his outlook on undocumented immigrants.

"Mexican immigrants, as with all immigrants, have much lower crime rates than native born. Eg El Paso safest city in U.S. Trump wrong," Murdoch tweeted.

Mexican immigrants, as with all immigrants, have much lower crime rates than native born. Eg El Paso safest city in U.S. Trump wrong.

Murdoch's remarks were in response to Trump claiming undocumented immigrants from Mexico are mostly criminals. The mogul didn't stop there, he posted a second tweet further challenging Trump's assertions.

"So FBI says 267000 illegal aliens incarcerated. Who are the other two million presently incarcerated?" Murdoch tweeted.

So FBI says 267000 illegal aliens incarcerated. Who are the other two million presently incarcerated? Seems like social breakdown.